Quite a lot of design parameters exist when the designer designs the best performance impeller and guidevane. Finally, it is necessary to decide the detail 3D shape of impeller and guidevane. The best flow conditions of the flow velocity and the flow angle at the impeller inlet and outlet are designed as first step before impeller detailed 3D shape is designed. The detailed 3D shape is not necessary in this study. The optimum meridian shape has been found, assuming that the total loss head is addition of the blade-to-blade diffusion loss head and the hub-tip axial-symmetrical annular surface friction loss head. That is, the meridian shape is mainly decided depending on the blade-to-blade flow condition on hub surface, mean surface and tip surface. Main design parameters that decide the meridian shape is built in the loss head equation by diffusion factor and all the design parameters relate closely respectively. The value of the design parameters can be set at random for loss head calculation in a usual optimization technique. But, the loss head in the combination of the limited value design parameters can be calculated in this method. Therefore, the great change of design parameter value is not permitted in this optimum process, and the increment of all the design parameters is set respectively and the optimization of the design parameter is advanced from an initial value of the design parameters changing the value of design parameters little by little. Therefore, there is a possibility that the best solution becomes a local best solution and the influence of an initial condition value cannot be removed. In this method, it is necessary for coming out from the local best solution that the value of all the design parameters changes from an initial value to a largely different value. The specific speed influences all the other design parameters. So, the specific speed is changed gradually in restriction optimum process. In FEDSM2014-21030, the impeller blade number was assumed to be a variable real number design parameter and the specific speed that was the specification as constant value become a variable design parameter equally to other design parameters.

In AJK2015-09034, the impeller outlet diameter and impeller rotational speed were assumed to be a variable optimum design parameters. As a result, all the design parameters became variable. Optimization was executed from two different initial conditions to study the initial value dependency whether the obtained two optimum solution became the same. In FEDSM2016-7518, one initial value of the specific speed was assumed to be 916 and it was confirmed to obtain the solution from the specific speed 200 to the specific speed 3000 as the variable wide range design parameter by restriction. The design parameter of mixed flow angle of impeller inlet was not change at the beginning of calculation and changed rapidly in the latter half of the calculation. The cause of the mixed flow angle of impeller inlet value jump was uncertainty. In FEDSM2017-69024, the influence of the surface roughness of the axial-symmetrical hub and tip wall was examined. The impeller blade number, the guidevane blade number and mixed flow angle of impeller inlet were able to change by restriction, and the influence of the impeller blade number and the guidevane blade number was examined. The mixed flow angle of impeller inlet was assumed 0 degrees (axial-flow) to avoid the parameter value jump. In this paper, the specific speed design parameter become the restriction design parameter. The specific speed as restriction parameter has been changed from the lower bound value to the upper bound value to come out from a local best solution. The efficiency extended to the specific speed whole area is able to be improved by the influence of the another middle specific speed with the highest efficiency. It is found that the value of the change increment at the specific speed as restriction parameter is important very much executed by the several kind of specific speed increment. In order to improve the design parameters of traditional impeller and guidevane in the future, it is convenient that total head and flow rate are new optimum design parameters instead of impeller outlet diameter and impeller rotational speed. The impeller rotational speed can be calculated by specific speed and total head.

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